Label Placement in Road Maps

A road map can be interpreted as a graph embedded in the plane, in which each vertex corresponds to a road junction and each edge to a particular road segment. We consider the cartographic problem to place non-overlapping road labels along the edges so that as many road segments as possible are covered by labels. We show that this is NP -hard in general, but can be solved in polynomial time if the road map is an embedded tree. Moreover, we give an efficient approximation algorithm for general road maps, assuming that each individual road can be labeled optimally in polynomial time.